The present invention relates to asymmetrical microporous fibers, particularly for the treatment of blood, and made up of a first polymer which is hydrophobic and a second polymer which is hydrophilic. Furthermore the invention relates to a process for the manufacture of such fibers, in which the polymeric components are dissolved in a polar and aprotic solvent, the solution so produced is extruded through a spinnerette to form a hollow fiber structure into whose lumen a precipitant is introduced and the resulting hollow fiber is placed in a bath to free it of components that are able to be washed out.